Improving the risk management process in quality management systems of higher education

The purpose of this paper is to improve the risk management process in the quality management system of higher education, taking into account the hazardous factors that increase the probability of occurrence and severity of consequences of undesirable events, as well as favorable factors that reduce the probability of occurrence and severity of consequences of hazardous events. The basis of risk management in the quality management systems of higher education institutions is the “Bowtie” method, which involves six main steps of identifying inconsistency, determining the impact of hazardous and favorable factors according to the impact group, ranking hazardous and favorable factors, calculating risk, substantiating precautionary measures and checking calculations. To rank hazardous and favorable factors, the authors used the “Decision Making Trial and Evaluation” method (hereinafter—DE-MATEL), which is based on paired comparison and decision-making tools based on graph theory. An improved process is proposed for risk assessment, which differs from the known ones by the presence of the identification of the cause-and-effect relationship “hazard (inconsistency)-hazardous event-consequences”, identification of hazardous and favorable factors of the internal and external environment that affect the probability and/or the degree of severity of a hazardous event—the appearance of an inconsistency, which is carried out after the inconsistency has been determined; determination of causal hazardous and favorable factors by an acceptable method. Registers of inconsistencies (hazards), hazardous and favorable factors have been developed and proposed based on the requirements for accreditation of educational programs and the international standard ISO 9001:2015, which will allow, based on a risk-oriented approach, to provide a basis for setting the goals of a higher education institution under martial law in order to guarantee effective implementation of the mission and strategy. They are proposed for decision-making in the quality management systems of educational organizations on the substantiation of precautionary or corrective measures based on ranking the risks from identified inconsistencies, which are determined taking into account the impact of the entire set of identified significant hazardous and favorable factors. The value of this paper is to improve the quality risk management process in educational organizations, taking into account the impact of hazardous and favorable factors, and to develop an appropriate step-by-step algorithm of actions and a risk assessment form.

Table 1.International standards of the quality management system in education.The standard is adapted to the so-called high-level structure, a basic structure with single main texts for the central requirements for management systems, as well as common designations and definitions, which was the basis for all management system standards.The standard considers the "Context of the organization", that is, the internal and external environment of the company, the requirements of the relevant stakeholders, the emphasis is placed on the responsibility of the top management, a risk-oriented approach is introduced, which replaces, among other things, the so-called preventive measures, hazard identification, risk assessment and opportunities An Argentine standard that explains the application of the requirements of ISO 9001 to educational institutions and the interpretation of these requirements in terms used in education prevention of negative impacts 10,11 .Hence, there is a need to develop a clear, efficient and effective risk management process, which is an urgent task due to the multifaceted nature of the problems faced by universities and a significant number of approaches that can be applied to solve them.It should be noted, based on a number of scientific studies 12,13 , that the implementation of quality management system in a higher education institution based on 9001:2015 requirements leads to several unresolved issues: for example, there is no clear methodology of risk management specifically in educational organizations with the specificity of training applicants whose quality of skills cannot be simultaneously tested (for example, new knowledge are found, a different vision that does not correspond to existing scientific paradigms 14 ), or there are no recommendations regarding the level of organizational culture at which the requirements of the specified standard will be effective and will be implemented.
Analysis of scientific research over the past years has shown an increase in interest in ensuring the sustainability of educational institutions in emergency situations, which is connected with the global spread of the pandemic and the need to transfer education to a distance format 15 .The largest number of studies is devoted to the identification of risks during the provision and organization of distance learning.In particular, the authors 16 paid attention to the stability of communication, the adverse effect of technological zones near computers, the lack of physical contact between teachers and students, and the overloading of students with online tasks.
At the same time, in the analysed work, the conclusions drawn were based on an online questionnaire of the participants of the educational process, which contained a limited number of hazardous factors (hereinafter-HF), which does not allow us to talk about a comprehensive assessment of the problem.In other studies, attention was focused on the study of negative consequences when using information technologies in the management system of an educational institution 17 .The authors, using their own eight-step algorithm, analysed problem areas of information systems and developed recommendations for reducing the negative consequences of various failures.However, the paper considered only the area of management of the educational institution, while the educational process itself and its provision was omitted.
We note the fact that in the domestic space, a fairly significant number of publications are devoted to the risks and challenges of reforming both secondary and higher education, taking into account the need for digitalization of the educational process [17][18][19] .For example, in the papers 20,21 , the authors analysed the risk factors and identified the biggest of them: low-quality Internet and lack of information and communication tools for learning, which is the biggest threat to distance learning.Another paper 22 systematized and singled out the groups of external and internal risks of educational activity, comprehensively revealed the system of external risks and proposed possible mechanisms for responding to them, outlined the range of losses (economic, social, political and pedagogical) that are the result of the occurrence of risky events.And also the main conclusion drawn from the publication is the need for the effective implementation of educational activities in the field of higher education, for higher education institutions to timely identify and identify risks, which will help reduce the level of uncertainty in the activities of educational institutions, to determine the direction of movement on which it is necessary to focus managerial, personnel, methodological, research, financial, technological and organizational resources.The authors of the article 23 revealed the need to apply a risk-oriented approach to the implementation of the quality management system of higher education institutions, and also systematized groups of internal risks in the course of operational processes in the activities of higher education institutions and proposed possible mechanisms for responding to them.
The conducted analysis shows that it is possible to apply a risk-oriented approach to the management processes of educational institutions only from the position of making managerial decisions to achieve quality goals, when the manager determines opportunities and associated risks 24 .However, there are issues related to the limitation of resources, which requires the elimination of existing deviations or errors in risk assessments that will lead to unwanted financial losses.Moreover, in the processes themselves, risk is proposed to be determined in relation to potential events that are influenced by groups of different factors or their combination 25 , and therefore, in order for organizations to carry out a qualitative or quantitative assessment of risk and make appropriate management decisions, it is necessary to develop an appropriate management process risks.The authors of the publication 26 suggest using the improved AHP methodology to assess the risks and opportunities of the quality development of higher education from the point of view of ISO45001:2018 as the case study of higher education institutions in China.
Thus, the conducted research analysis shows that there are several directions of quality assurance in higher education institutions: curricula, criteria and rules for assessing students, quality of teachers and educational process, quality of material-technical and information resources, as well as collection, analysis and use of information 27 .At the same time, ensuring the quality provision of educational services involves systematically identifying and managing the various processes encountered in educational organizations 28 .This is mainly done by applying a management system based on the PDCA cycle with a general focus on risk-oriented thinking, the key element of which is the implementation of necessary actions to achieve the planned measures and results based on risk management, requiring the effective process development.
The aim of this paper is to improve the risk management process in the quality management system of higher education in accordance with the requirements of 9001:2015, ISO 21001:2018 and other standards, taking into account HFs, which increase the probability of occurrence and severity of consequences, as well as FFs, which reduce the probability of occurrence and severity of consequences from hazardous events.

Materials and methods
The most common approach to risk management in the quality systems of any organization, which is the basis for developing an action plan to achieve the desired result and identifying the resources required for the effective and efficient functioning of each process, is the "Bowtie" method 29 .This is the most common model, the popularity of which is attributed to the convenience and simplicity of presenting the cause-and-effect relationship between hazard, hazardous event and consequences.The visualisation of this model helps to clearly demonstrate the risk management process by determining the number of barriers (protective or precautionary measures) that are placed on the path between a hazard and a hazardous event, as well as between a hazardous event and its consequences.The number of barriers makes it possible, on the one hand, to estimate protective or precautionary measures for occupational safety, and on the other hand, to influence the probability of the hazardous event occurring.The latter is determined by the "as low as reasonably practicable" (ALARP) principle, according to which the residual risk level should be reduced as much as possible 30 .
It makes it possible, in general, to understand the reasons for the occurrence of a hazardous event from the presence of certain inconsistencies in any process or threats (challenges) to the organization and to assess the consequences of their occurrence, which is the basis of risk calculation.This method also allows you to justify the financial costs of the risk management process based on the analysis of the efficiency of the created protective barriers that are placed on the path from inconsistency to a hazardous event, as well as between a hazardous event and its consequences (Fig. 1).
This approach is characterized by the ability to take into account the influence on a change (increase or decrease) in the probability of occurrence and the severity of the consequences of a hazardous event of various external and internal hazardous and favorable factors (Fig. 2), which are proposed to be divided into seven groups: human, technical, organizational, economic, social and pedagogical, martial law (Fig. 3).In this case, hazardous factors (HF) influence an increase in the probability of occurrence and/or severity of consequences of a hazardous event and, as a result, an increase in risk, which is a loss of effectiveness, especially in quality management systems.Favorable factors (FF) have an impact on reducing the probability of occurrence and/or severity of consequences of a hazardous event and, ultimately, on reducing the risk together with protective or precautionary actions (measures), which is the improvement of effectiveness, especially in the quality of providing the educational process.
An improved risk management process consisting of six main steps is proposed for risk assessment (Fig. 4).The main difference between the proposed process and the known ones 27,[31][32][33] is identification of the causeand-effect relationship "hazard (inconsistency)-hazardous event-consequences", identification of hazardous and favorable factors of the internal and external environment, which affect the probability and/or degree the severity of the hazardous event-the appearance of an inconsistency, which is carried out after the inconsistency has been determined; determination of causal (ignoring consequential) HFs and FFs by an acceptable method (for example, DEMATEL or ANP).
The first step is devoted to determining the cause-and-effect relationship between "hazard (inconsistency)hazardous event-consequences" in the quality system of higher education, which can lead to the occurrence of a hazardous event under certain conditions, for example, a low level of training of higher education students.The result of inconsistencies can be seen as the loss of the image of the university, the number of applicants, financial support, personnel potential, and others (Table 2).This step requires the creation of an appropriate catalogue of hazards (inconsistencies), which are violations of the requirements of legislation in the field of education (higher education standards).The basis of its creation is a survey of interested parties, who are invited to provide an answer that affects the process of quality training of students.For example, the Table 3 provides the list of inconsistencies (threats) compiled on the basis of the requirements for accreditation of educational programs.
In the second step, we determine the HFs and FFs, from which we also form the corresponding register (Tables 4, 5).In the given example, HF hazards (inconsistencies) include: non-fulfilment of the requirements for accreditation of educational programs, non-fulfilment of the requirements for the evacuation of applicants to a bomb shelter during an air raid alert, non-fulfilment of the requirements for traineeships of students at production enterprises-low competence that affect the probability of occurrence and degree of severity losses from this hazard The list of HFs and FFs is determined based on the development of various studies on the problems of management of higher education institutions, surveys of experts in this field, interviews with the institution management and staff.Please note that the list of HFs and FFs in each institution of higher education may differ, based on the specific circumstances that have developed in it.In addition, such a determination of HFs and FFs must be made for each hazard (inconsistency).
In order to identify the impact of HFs and FFs on the probability and severity of consequences of a hazardous event occurring due to one or another inconsistency, a process of surveying of all interested parties (teachers, students, employers, management of a higher education institution, technical workers, etc.) is carried out.They are offered to choose one or another HF and FF in an online questionnaire (Fig. 5).The above excerpts are from a survey conducted at Dnipro University of Technology, located in the city of Dnipro, Ukraine, in the period from February to June 2022.The survey involved 112 people (43 men and 69 women) aged between 18 and 43.The majority of participants (70%) are university lecturers, 22% are applicants and 8 are employees of various departments.In this case, the average work experience of teachers is 12.4 years.Their scientific field of activity is related to mining (33.2%), construction (26.8%), service sector (31.4%), economics (4.2%), ecology (14.6%).
The result of such a procedure is the formation of a register (Table 6) of the most influential HFs and FFs on the determined inconsistency, which are then ranked to identify the most important ones.This procedure will be conducted by several recognized experts representing the management of the institution, teachers and at least 5 applicants.
In the third step, we study the interaction of HFs and FFs with the identified hazards (inconsistencies) and use the "Decision Making Trial and Evaluation" (DEMATEL) method, which is based on paired comparison and decision-making tools of graph theory 34,35 , which will allow us to transform cause-and-effect relationship in structural-visual models and identify and understand the interdependencies between different HFs and FFs that will lead to negative consequences.Relationships between influencing factors are made on the basis of paired comparison.
This case study involved five experts certified as internal or external auditors of quality management systems in accordance with the requirements of the ISO 9001:2015 international standard and the ISO 19011:2018 provisions; work experience in an educational organization is for at least 5 years; degree of education-the level is not lower than Doctor of Philosophy; they also have relevant documents certifying their training and knowledge of standards: standards and recommendations of the European Higher Education Area ESG-2015; ISO 21001:2018 "Educational organizations-Management systems for educational organizations-Requirements with guidance for use"; 31000:2018 "Risk management.Principles and guidance", and knowledge of the expert activity specifics; criteria and indicators of the effectiveness of an expert on the quality of education in EU countries .They are experienced in conducting expert examinations and audits.
To determine the degree of impact between various negative (positive) factors, criteria with a five-level scale are used, consisting of verbal expressions and corresponding fuzzy numbers (Table 7).www.nature.com/scientificreports/ The n × n pair comparison matrix is formed according to experts using the paired comparison method, which is a natural way and is consistent with human intuition and general way of thinking 39 .In this case, a data consistency check is applied using the following formula: where m is criteria number, k is number of experts, d is the average value of the direct influence of criterion i on j.If the average consensus gap coefficient value is less than 0.05, we consider the expert's assessment as stable 40 .
Variable H stands for number of experts; n is the number of considered criteria.The comparison between two factors i and j by expert k is shown as b k ij .According to the fuzzy theory in Table 7, the value of "zero impact" is 0, "very low impact" is 1, "low impact" is 2, "high impact" is 3, and "very high impact" is 4. As a result, with an independent assessment of each expert, the response matrix is formed by Eq. (1).Given that each component does not affect itself, the diameter components of each response matrix B (k) are equal to zero: The average matrix A = a ij n×n has a direct impact on the matrix and the average value of expert ratings, which can be calculated according to Eq. ( 2).This matrix represents the direct impact of each criterion on the other criteria: Matrix D can be calculated using Eqs.( 3) and ( 4): www.nature.com/scientificreports/ The matrix T c can be calculated according to Eq. ( 5).In this equation, I is the identity matrix.Each element of the matrix T c can be formed with respect to a fuzzy number τ ij = l t ij , m t ij , u t ij .Given Eqs. ( 5), ( 6), ( 7) and (8).D 1 , D m , D u are all matrices n × n.Table 6.Forms for the register of HFs and FFs that increase/decrease the probability of a hazardous event occurring.

Identification of the causal relationship "Hazard-hazardous event-consequences" HF FF Inconsistency Hazardous event Negative consequences
Non-compliance (e.g.failure to meet any requirement or accreditation requirements) Loss of accreditation Loss of income from training according to this accreditation Table 7. Verbal expressions and corresponding fuzzy numbers [36][37][38] .

Final equivalent Description Fuzzy equivalent
Very high impact VH 0.75 1 www.nature.com/scientificreports/To determine the effect and relevance of the criteria, the matrix T c must be fuzzy first.Equation ( 9) will be used so that there are no fuzzy T c matrices.
The action and relevance of criteria are determined using r and c values.The values of Eqs. ( 10) and ( 11) can be calculated: r is the sum of row i, and c is the sum of column j of the matrix T c .r shows the total effect of direct and indirect influence of i on other criteria, and c shows direct and indirect total influence of factor j on other factors.
As a result, r + c indicates the importance of criterion i in the system.r − c shows the effect of criterion i in the system.If r − c is positive, the action of criterion i belongs to the group of causes, and if r − c is negative, the effect of the criterion, which belongs to the group of "dependents".
The next step of the procedure is a risk analysis, which involves determining the probability and degree of severity of a hazardous event from the action of the causative HF.For this purpose, appropriate scales have been determined based on the recommendations of the ISO 73:2018 standard, which are summarised in Tables 8 and 9.
Next, the risk level is calculated for each HF and FF as the product of the probability of a hazardous event (B) and the severity of the consequences (T) from all predetermined most significant HFs and FFs: The risk from hazardous factors is determined by the formula: The risk from favorable factors is determined by the formula: The total risk from exposure to HF and FF is determined from: (8) Table 8.Probability levels (B) of the occurrence of a hazardous event.

Gradation of the level of influence
The probability level of HE Characteristics of probability (description) The training of students takes place in accordance with the regulatory requirements of educational standards, the students have a high level of training, the shortcomings or inconsistencies identified have a certain impact on the quality of the students' training, but their influence is due to the personal qualities of the students 3 Moderate The training of students takes place in accordance with the normative requirements of educational standards, the students have an average level of training, the shortcomings or inconsistencies identified affect the quality of the students' training, leading to clear gaps that require further non-essential reorganization of the educational process for the training of students 4 Significant The training takes place in violation of the requirements of educational standards, the students have an average level of training, shortcomings or inconsistencies identified affect the quality of their training, leading to gaps that require the introduction of appropriate changes in the educational process where P + i ; P − i are the risk from the i-th hazardous/favorable factor, respectively B + i ; B − i are the probability of occurrence/non-occurrence of a hazardous event from the i-th hazardous/favorable factor; T + i , T − i are the severity of consequences of the occurrence/non-occurrence of a hazardous event from the i-th hazardous/favorable factor; P i is the total risk from exposure to hazardous/favorable factor.
The risk assessment form in the quality system is given in Table 10.
After determining the level of risk (Table 11), solutions are proposed for preventive actions to reduce it.According to the results of determining the risk level, it can be assigned to one of the risk groups: -I, it is necessary to stop the activity of determining and implementing preventive and protective measures to reduce the risk to an acceptable level; -II, it is necessary to define and implement preventive and protective measures to reduce the risk to an acceptable level in case of partial cessation of activity; -III, no risk reduction measures are required, but hazard control is required; -IV, no risk reduction measures are required and no hazard controls are required.
Very often, the protective measures taken reduce the probability of the risk, but do not eliminate the hazard.In these cases, the probability of risk decreases, but its severity remains unchanged.It is also necessary to consider preventive actions aimed at reducing the severity of the consequences.If the level of risk is totally unacceptable and unacceptable, we understand that it is forbidden to carry out work without changing the conditions and without developing and implementing measures to reduce risks.First of all, preventive and protective measures should be implemented to prevent the realization of the hazard in the HE and/or to reduce the consequences of the HE.Control over the prohibition of works is established.It should be noted that the risk acceptance criteria given in Table 11 are notional and need to be assessed in each organization that tries to implement the described approach, as "they are based on the internal and external context and objectives of the organization, and they may arise from laws, policies, standards and other demands 41 .The most common and flexible framework used for risk criteria divides risks into the three groups mentioned above: "unacceptable area", "ALARP area" and "acceptable area" 42 .( 14) 10.An example of a form for determining the risk levels from HFs and FFs.

Influence on the probability of occurrence of a hazardous event from HF
The severity of the occurrence of the hazardous event of the i-th HF

The level of risk from HF-i
Non-compliance Loss of accreditation Total OR of hazard j from all n of HF and FF Rп j = ∑ R -п j1 -∑ R + п j1

Results
Take, for example, an educational training program for second-level Master students, where only HF is considered as an example.But the same approach is applied to FF.The list of its inconsistencies is formed based on the analysis of the results of the internal audit, in accordance with the requirements of ISO 9001:2015 or external accreditation of the educational program by experts of the National Agency for Quality Assurance of Higher Education.The result of the work is a catalogue of inconsistencies (Table 12).The next step is to introduce a procedure for surveying all interested parties to identify the most influential HFs that increase the probability of occurrence and the severity of the consequences of a hazardous event.For example, for the specified educational program, taking into account its implementation in the conditions of martial law, the experts chose from the list given in Table 3 twelve HFs, which are shown in Table 13.
Next, they are ranked using the DEMATEL method, where experts make paired comparison of the identified HFs, filling in the corresponding table (Fig. 6) in the Excel program.The dimensions of the matrix are determined by the number of HF (A12), which affect the appearance of a specific hazardous situation.Experts compile a matrix based on a subjective assessment of the greatest interaction with other indicators.In this case, the judgment is usually based on the interdependence of HF and inconsistencies.It is estimated that all HFs from each group will lead to a hazardous event and, in general, will harm the educational process.In addition, when compiling the matrix, experts are invited to take into account the possibility of controlling the manifestation of HF.
Further, the obtained results are processed using the appropriate mathematical apparatus, which is also performed in the Excel program, which allows obtaining HF prioritization (Table 14).
As a result, on the basis of a detailed analysis of the impact of HF, we obtain their prioritization, based on establishing the degree of importance and the level of impact on the occurrence of a specific hazardous event.Thus, in the given example, considering the inconsistency of H 14 "Teachers do not have appropriate qualifications", it was established that the greatest influence is exerted by HF under the number A 40 , A 43 , A 41 , A 44 , A 27 , A 1 .At the same time, a negative sign in the impact level column indicates that they will have a greater impact on the magnitude of the consequences of the occurrence of a hazardous event.In a similar way, the FF analysis is conducted.
The constructed prioritization of HF compatible with their ranking allows obtaining a map of connections between HF dimensions (Fig. 7) that visually shows their interdependence.
Determining the causal HFs and, as a consequence, FFs obtained during a similar procedure using the DAMTEL method allows moving to the step of calculating the risk from exposure to significant (causal) HFs (Table 15) and FFs (Table 16).As a result, we obtain risk values which, under certain conditions, that is, when Table 12.Fragment of analysis of inconsistencies as a result of examination of the educational program by experts of the National Agency for Quality Assurance of Higher Education.

No.
Criterion Inconsistencies found by the expert group 1 Criterion 2. Structure and content of the educational program H 3 .In the educational program, the structural and logical scheme does not reflect the relationships of the educational components 2 Criterion 5. Control measures, evaluation of higher education students and academic integrity H 9 .Forms of control and evaluation criteria for higher education students are unclear and not understandable 3 Criterion 6. Human resources H 14 .Teachers do not have appropriate qualifications and/or professional experience and are unable to ensure the implementation of educational program Table 13.Fragment of the results of the processing of the questionnaire of interested parties to detect the HF, which increase the probability of the occurrence of a hazardous event during martial law.hazardous and favorable factors coincide, can compensate each other, thereby reducing the risk level in quality management systems.The issue of interaction between various factors is not simple, as it requires careful verification and the experience of experts who will conduct the appropriate analysis.Of course, specific recommendations for compensating for negative factors with favorable ones can be made only in case of a thorough study of organizational culture, understanding of social-psychological phenomena occurring in the company: relationships, connections, beliefs, politics, activities and relationships of groups 43 .Since the total negative risk j from all n of HFs is equal to 122 (see Table 15), and the total positive risk j from all n of FFs is equal to 27 (see Table 16), in this case, taking, as a rough approximation, a linear relationship between the impact of HFs and FFs, the total risk in the quality management system will be equal to: Although the proposed approach is not perfect, it does provide an overall measure of risk based on an integrated process that reflects the constructive confrontation of opposing factors.As a result, a creative solution to reduce the risk level is generated in the form of, perhaps even a new idea, as it becomes possible to comprehensively analyze the cause-and-effect relationships between the inconsistency and specific causal hazardous and favorable factors.Moreover, the proposed approach makes it possible to determine the most influential factor and further work with it: in case of a negative impact-by determining precautionary or preventative actions, and in case of a favorable factor-ways to enhance its influence.
The basic requirement for applying this approach is the need to adhere to standard academic training protocols, such as compliance with all rules and assumptions made, a clear basis for all choices, etc.In addition, the educational environment should meet reliability and validity criteria.The reliability requirement here refers to the degree to which a risk assessment produces the same results when analyzed repeatedly, and the validity requirement refers to the degree to which a risk assessment describes the specific concepts that it attempts to describe.Having accepted these criteria, results (beliefs), the value of the calculated risk level can be considered to a certain extent as justified 44 .www.nature.com/scientificreports/

Discussion
In the described process of risk management, the most important component is the identification of inconsistencies (hazards) and HF, which involves a thorough investigation of the cause and sources of risk, as well as events and situations that can significantly affect the overall results in relation to the goals of the educational process.It is expected that risks will be studied and predicted at each stage of the educational process, based on key performance indicators established in the higher education quality assurance system, which is also emphasized in the research paper 27,45 .Such an approach requires systematic effort on identifying inconsistencies by constructing a monitoring system that assesses risks at specified intervals and facilitates the revision of precautionary measures depending on the current situation.A similar approach is implemented in Ref. 32 , but the difference of the proposed one is the involvement of a wide range of interested parties, which is one of the most important conditions for the formation of a high-quality educational process [46][47][48][49] .It is through the elaboration of both external and internal inconsistencies, and most importantly, proposals (opportunities), there are real ways to substantiate relevant managerial decisions based on the financial capabilities of educational institutions 27,50 .
Taken together, identifying inconsistencies of hazardous factors, opportunities, creating a register of them that will be constantly updated, identifying significant threats (for example, due to a pandemic, military operations, economic challenges, natural disasters) 51,52 , constructing cause-and-effect relationships between a threat (including in relation to the educational environment, teaching methods, etc.)-a hazardous event (for example, loss of accreditation, low-quality educational services, etc.) and consequences, taking into account all additional components (significant hazardous factors, opportunities), is the foundation for conducting the justification of effective precautionary and protective measures 53,54 , and most importantly, readiness for changes and upcoming challenges [54][55][56] .It is the construction of such a system that will make it possible, in the future, based on the construction of even the simplest models 57,58 , to predict the development of events and ensure readiness to respond to challenges 59,60 .The more detailed the current state that has developed at a specific point in time in the quality system of a conditional university 61,62 is analyzed, the more opportunities there are for adopting appropriate ways of developing the educational environment, meeting the needs of interested parties, and most importantly, creating a safe environment, the potential of which will reveal the opportunities of participants in the educational process (both teachers in terms of ensuring academic freedom, and applicants, if possible, to reveal the relevant abilities that will be in demand in the labor market).
Despite the significant proposed approach publicity, it has significant advantages over the existing ones, as it allows a more thorough study of the occurrence of a hazardous event from the combined action of several factors.In addition, when compiling appropriate registers, experts analyze all the causes of the hazardous event occurring, assess the effectiveness of existing monitoring tools, which is the basis for savings through the redistribution of already existing resources 13 .
The strengths of the above approach include an integrated approach to the implementation of corrective actions, which is expressed in comprehensive monitoring and assessment of results, partnership among all interested parties, taking into account the impact of negative and favorable factors on the risk level.In addition, this allows analyzing the processes at the university in terms of the effectiveness of their functioning, which helps to create conditions for systematic educational process management, as opposed to intuitive control (based on tradition, trial and error).
Given that the risk management process is defined as "a planned and structured process aimed at improving the effectiveness of decision-making to ensure the appropriate activity of higher education institutions at a certain time 63 , there is a need to understand their consequences, which can be done through the construction of cause-and-effect relationships between challenges and possible hazardous events.In this case, to determine the "probability" of the hazardous event occurring, it is important to use a multivariate analysis 33,64 .Currently, there are powerful quantitative methods for assessing risks, such as Bayesian networks, but they are much more complex than the Bowtie method, and on the other hand, they require appropriate additional research to identify the relationships between various hazardous factors.We believe that Bayesian models are the next step in improving quality systems, since artificial intelligence can be used to perform the appropriate analysis.
Despite the considerable proposed approach is quite cumbersome, it has significant advantages over the existing ones, as it allows for a more thorough investigation of the occurrence of a hazardous event 65 from the combined action of several HFs.In addition, during the compilation of relevant registers, experts analyse all the reasons for the occurrence of a hazardous event, evaluate the effectiveness of existing control measures, which is the basis of savings due to the redistribution of already existing resources.
It should be noted that most of the relevant HFs are interdependent, which is also taken into account during the implementation of the given approach.The more relationships are established, the higher the score will be compared to other HFs.
In general, referring to the requirements of the international standard ISO 9001:2015, there is a need to introduce a policy of the quality management system of higher education under martial law, which is based on the culture and traditions of the higher education institution, a set of beliefs and values that determine the behavior of the educational institution, which is aimed at minimizing risks 66 .
The significance of the presented research lies in its practical use in educational institutions facing the choice of the optimal methodology for applying a risk-oriented approach in education quality management systems.The shortcomings of the study include the influence of subjectivity at the first stages of the risk management process, which is characteristic of expert methods, when forming from the relevant registers, determining the dependence between inconsistency and HF.However, in the future, the application of a mathematical approach to risk ranking will allow us to identify inappropriate relationships and return to the revised previous steps of HF identification, which are associated with a specific inconsistency.

Conclusions
The improvement of the risk management process in the system of higher education of students under martial law is based on the sequence of six main steps and differs from known processes by the presence of the identification of the cause-and-effect relationship "hazard (inconsistency)-hazardous event-consequences", identification of HFs and FFs (hazards-inconsistencies) of the internal and external environment, which affect the probability and/or degree of severity of a hazardous event-the occurrences of inconsistency, which is carried out after determining the inconsistency; determination of causal (ignoring consequential) HFs and FFs by an acceptable method (for example, DEMATEL or ANP).
The developed and described registers of inconsistencies (hazards), as well as HFs and FFs, based on the requirements for accreditation of educational programs and the international standard ISO 9001:2015, etc., using a risk-based approach, provide the basis for transforming the goals of a higher education institution in conditions of martial law in order to guarantee the effective implementation of the mission and strategy of the relevant requirements.
It is proposed to determine the criteria for risk analysis, which involves establishing the probability and degree of severity of a hazardous event from the action of the causal HFs and FFs impact, to use the cumulative effect of the causal HFs, as well as FFs, which is calculated as the sum of their effects.
Flexible forms that can be used by institutions of higher education are offered for the initial assessment of negative risks of HF hazards, prioritization of HFs and FFs based on the degree of importance and level of impact, analysis of inconsistencies as a result of the examination of a conditional educational program, a questionnaire to establish the impact of HFs and FFs on a specific inconsistency without changes or after adaptation in accordance with the specifics of the relevant higher education institution.
2015 Quality management systems-Requirements International Organization for Standardization

Figure 1 .
Figure 1.Risk management procedure in educational quality management systems based on the "Bowtie" model.

Figure 2 .
Figure 2. Hazardous and favorable factors that lead to an increase in the probability of a hazardous event occurring.

Figure 3 .
Figure 3. Hazardous and favorable factors that lead to an increase in the probability of a hazardous event occurring.
of requirements for accreditation of educational programs Loss of accreditation of educational programs Decrease in income, loss of reputation 2 Failure to comply with requirements to evacuate students to a bomb shelter during an air raid alert Missiles and drones of the aggressor, or parts of them shot down by the air defence system of the Armed Forces of Ukraine, hit the building of an educational institution Loss of health and life of teachers; students Loss of reputation of the educational institution 3 Loss of reputation of the educational institution Employers' refusal to employ graduates of an educational institution Unemployed graduates of an educational institution Loss of reputation of the educational institution Vol.:(0123456789) Scientific Reports | (2024) 14:3977 | https://doi.org/10.1038/s41598-024-53455-9

Figure 5 .
Figure 5. Fragment of a form for determining the influence of hazardous and favorable factors that increase the probability of a hazardous event occurring from a specific hazard (inconsistency).

Figure 6 .
Figure 6.An example of a paired comparison matrix filled in by one of the experts.

Table 2 .
Examples of identification of the cause-and-effect relationship "hazard-hazardous eventconsequences".

Table 3 .
Fragment of the list of hazards (inconsistencies) in educational programs.

Table 4 .
Example of HF risk in the quality system of an educational organization.GF group of factors.

Table 5 .
Example of FF risk in the quality system of an educational organization.GF group of factors.

Table 9 .
Levels of severity of consequences of (T) HE.

Table 11 .
Criteria for risk acceptance.

Table 14 .
Prioritization of HF based on degree of importance (r + c) and level of impact (r − c).

Table 15 .
An example of a form for the initial assessment of occupational risks from HF.

Table 16 .
An example of assessing the risks from FF.